And have Mathematica reason about the Big-Oh running time somewhat is the hard part :D
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belisariusJul 11 '12 at 2:56

If everything is polynomial you might get away with minBigOh[p1_, plist_List] := PolynomialReduce[p1, plist][[2]] (which is in keeping with the "term-rewritica" moniker).
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Daniel LichtblauJul 11 '12 at 15:41

Isn't there some simple validity to the method I propose? When does it fail?
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Mr.Wizard♦Jul 11 '12 at 12:06

@mr.wizard not near mma now, but I would say something like MinBigOh[10 x, 1/10^6 x^2] would fail for the specific answer. Of course, then you pick a bigger value to substitue, but you can always twiddle the coefficients to find a counter example and eventually you hit max/min machine number at which point you can no longer substitute. The objective is not whether which has a higher tunning time, but what the time complexity is.
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rm -rf♦Jul 11 '12 at 13:12

I've never seen O notation in that form/degree before. Some reading is in order I guess.
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Mr.Wizard♦Jul 11 '12 at 13:23

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